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Journal of Scientific Computing

Erschienen in:

01.04.2013

Meshfree Particle Methods in the Framework of Boundary Element Methods for the Helmholtz Equation

verfasst von: Christopher Davis, June G. Kim, Hae-Soo Oh, Min Hyung Cho

Erschienen in: Journal of Scientific Computing | Ausgabe 1/2013

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Abstract

In this paper, we study electromagnetic wave scattering from periodic structures and eigenvalue analysis of the Helmholtz equation. Boundary element method (BEM) is an effective tool to deal with Helmholtz problems on bounded as well as unbounded domains. Recently, Oh et al. (Comput. Mech. 48:27–45, 2011) developed reproducing polynomial boundary particle methods (RPBPM) that can handle effectively boundary integral equations in the framework of the collocation BEM. The reproducing polynomial particle (RPP) shape functions used in RPBPM have compact support and are not periodic. Thus it is not ideal to use these RPP shape functions as approximation functions along the boundary of a circular domain. In order to get periodic approximation functions, we consider the limit of the RPP shape function as its support is getting infinitely large. We show that the basic approximation function obtained by the limit of the RPP shape function yields accurate solutions of Helmholtz problems on circular, or annular domains as well as on the infinite domains.

Vorheriger Artikel High Order Stable Finite Difference Methods for the Schrödinger Equation

Nächster Artikel Efficient Numerical Methods for Strongly Anisotropic Elliptic Equations

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Titel: Meshfree Particle Methods in the Framework of Boundary Element Methods for the Helmholtz Equation
verfasst von: Christopher Davis
June G. Kim
Hae-Soo Oh
Min Hyung Cho
Publikationsdatum: 01.04.2013
Verlag: Springer US
Erschienen in: Journal of Scientific Computing / Ausgabe 1/2013
Print ISSN: 0885-7474
Elektronische ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-012-9645-0

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